According to the Yankee Group, 53% of all cable households rate cable companies

Question

According to the Yankee Group, 53% of all cable households rate cable companies as good or excellent in quality transmission. Sixty percent of all cable households rate cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted. a. What is the probability that more than 175 cable households rate cable companies as good or excellent in quality transmission? b. What is the probability that between 165 and 170 (inclusive) cable households rate cable companies as good or excellent in quality transmission? c. what is the probability that between 155 and 170 (inclusive) cable households rate cable companies as good or excellent in having professional personnel? d. What is the probability that fewer than 200 cable households rate cable companies as good or excellent in having professional personnel?

Explanation / Answer

Given total population N = 300

Given as per data, 53% cabe households have good transmission

p = 0.53

q=0.47

mean = 0.53*300 = 159

standard devaition = sqrt(300*0.53*0.47) = 8.644

a) the probability that

p(X>175)

Z = (X-u)/s

= (175-159)/8.645

= 1.85

p(Z>1.85), from Z table = (1-0.968) = 0.032

b) p(165<=x<=170)

p(165-159/8.645 <= Z <= 170-159/8.645)

p(0.694<Z<1.27)

=0.898 -0.7549

= 0.1431

c) p(155<X<170)

p(-0.46<Z<1.27)

= 0.5752

d) p(X<200)

= p(Z<4.2)

= is almost 1

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